Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
369 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 369 conjugacy classes of subgroups — too many to draw. Only its 76 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C4×GU(2,𝔽3) | C3 | direct (N × H) |
| 6. C3×C4×SL(2,𝔽3) | C4 | semidirect |
| 7. C3×GU(2,𝔽3) | C4 | direct (N × H) |
| 33. C4×SL(2,𝔽3) | C3×C4 | semidirect |
| 34. GU(2,𝔽3) | C3×C4 | direct (N × H) |
| 42. C3×SL(2,𝔽3) | C42 | semidirect |
| 108. SL(2,𝔽3) | C3×C42 | semidirect |
| 144. C3×C4 | GU(2,𝔽3) | direct (N × H) |
| 176. C4 | C3×GU(2,𝔽3) | direct (N × H) |
| 180. C3 | C4×GU(2,𝔽3) | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C4×#41⋊C3 | 2 |
| C2×C3×GU(2,𝔽3) | 2 |
| C4×GU(2,𝔽3) | 3 |
| C3×C4×#104 | 3 |
| C3×C4×C3⋊C8 | 4 |